Will I be eligible to do Ph. D through distance learning? I am currently in United States and completed my masters here.

Wellborn Group of Professional Studies has below criteria for taking admissions to it's various courses:

Courses	Eligibility
UG Diploma	Candidate must have passed 10th from a recognized board with Mathematics as a subject.
M.A.	Candidate must be a graduate from a recognized university.
BCA	Candidate must have passed 10+2 from a recognized board.
MCA	Candidate must be a graduate from a recognized university.
PG Diploma	Candidate must be a graduate from a recognized university.
MSW	Candidate must be a graduate from a recognized university.
BBA	Candidate must have passed 10+2 from a recognized board.
M.J.M.C.	Candidate must have passed 10+2 from a recognised board.
B.Sc.	Candidate must have passed 10+2 with science as a stream from a recognized board.
M.Com	Candidate must be a graduate from a recognized university.
MBA/PGDM	Candidate must be a graduate from a recognized university.

Wellborn Group of Professional Studies has courses such as B.Tech, M.A., BCA, MCA, PG Diploma, M.E./M.Tech, B.Com, BBA, M.J.M.C., M.Sc., B.Sc., M.Com, MBA/PGDM, M.Phil, Ph.D. which are primarily in the stream of Engineering, Humanities & Social Sciences, IT & Software, Business & Management Studies,

Hi. Candidate must be a graduate from a recognized university with minimum 50% marks. For information you can see below link https://www.shiksha.com/college/wellborn-group-of-professional-studies-lucknow-41295/course-bachelor-of-education-b-ed-206559 Thanks

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Yes, you can pursue B. Ed.